Riemannian Geodesic is Locally Minimizing

Theorem

Let $\struct {M, g}$ be a Riemannian manifold.

Let $\gamma$ be a geodesic.

Then $\gamma$ is locally minimizing.

Proof

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Sources

• 2018: John M. Lee: Introduction to Riemannian Manifolds (2nd ed.) ... (previous) ... (next): $\S 6$: Geodesics and Distance. Uniformly Normal Neighborhoods